Question

3.) A firm sells its product in a perfectly competitive market where other firms charge a price of $40 per unit. The firm's total costs are C(Q) 20+40+202. A. B. C. D. How much output should the firm produce in the short-run? What price should the firm charge in the short-run? what are the firm's short-run profits? What adjustments should be anticipated in the long-run?

Answer 1

Solution:

C(Q) = 20 + 4Q + 2Q², market price, P = $40

A. Marginal cost, MC(Q) = $\partial C(Q)/\partial Q$ = 4 + 2*2Q = 4 + 4Q

In short run, a firm in competitive market produces at point where marginal cost equals the market price.

Thus, at optimality, MC(Q) = P

4 + 4Q = 40

Q = 36/4 = 9 units

B. In short run, firm charges the price prevailing in the market, since under perfect competition, a firm cannot influence the market price. Thus, price charged = $40 per unit

C. With Q = 9, total costs for the firm = 20 + 4(9) + 2(9)²

TC = 20 + 36 + 36 = $92

Total revenue, TR = P*Q = 40*9 = $360

Profits (in short run) = TR - TC

Profits = 360 - 92 = $268

D. In the long run, seeing the firms earn a positive profit, more and more firms enter the market. With such increased supply, the market price falls down and finally reaches the average cost of the firm. By producing at this point, firms now earn 0 profit (or normal profits) in the long run.